radical extension

A radical tower is a field extension L/F which has a filtrationMathworldPlanetmathPlanetmath


where for each i, 0i<n, there exists an element αiLi+1 and a natural numberMathworldPlanetmath ni such that Li+1=Li(αi) and αiniLi.

A radical extension is a field extension K/F for which there exists a radical tower L/F with LK. The notion of radical extension coincides with the informal concept of solving for the roots of a polynomialPlanetmathPlanetmath by radicalsPlanetmathPlanetmathPlanetmathPlanetmath, in the sense that a polynomial over K is solvable by radicals if and only if its splitting fieldMathworldPlanetmath is a radical extension of F.

Title radical extension
Canonical name RadicalExtension
Date of creation 2013-03-22 12:08:35
Last modified on 2013-03-22 12:08:35
Owner djao (24)
Last modified by djao (24)
Numerical id 7
Author djao (24)
Entry type Definition
Classification msc 12F10
Synonym radical tower